About a month ago on a whim I picked up a crown tail Betta at Walmart. I had him in a one gallon fish bowel. Then I started to notice he wasn't moving around very much, and seemed lethargic. I upgraded him to a five gallon tank which has a filter and heater after researching. I read about tank mates for bettas and added a few ghost shrimp. A few days later they were gone. I didn't see any bodies, so I think my Betta must have eaten them?

I would like to add at least one other fish, but if he killed my ghost shrimp...

Glad your Betta is doing well. A 5g is not big enough, IMO, to have multiple fish, especially with having a male Betta. You could add a snail but keep in mind they tend to have big bio loads. I would suggest adding some more plants in your tank, Bettas love to have hiding places & leaves to rest on plus it'll make youre tank look more full if that's what you're wanting.